Conformal embeddings and simple current extensions

TL;DR

This paper explores the structure of intermediate vertex algebras arising from maximal conformal embeddings of reductive Lie algebras into semisimple Lie algebras of classical type, advancing understanding in algebraic structures.

Contribution

It provides new insights into the structure of intermediate vertex algebras linked to conformal embeddings, specifically in classical Lie algebra contexts.

Findings

Characterization of intermediate vertex algebras

Identification of conditions for conformal embeddings

Structural properties of simple current extensions

Abstract

In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.